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Simplifying 0.1v2 + v + -300 = 0 Reorder the terms: -300 + v + 0.1v2 = 0 Solving -300 + v + 0.1v2 = 0 Solving for variable 'v'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -3000 + 10v + v2 = 0 Move the constant term to the right: Add '3000' to each side of the equation. -3000 + 10v + 3000 + v2 = 0 + 3000 Reorder the terms: -3000 + 3000 + 10v + v2 = 0 + 3000 Combine like terms: -3000 + 3000 = 0 0 + 10v + v2 = 0 + 3000 10v + v2 = 0 + 3000 Combine like terms: 0 + 3000 = 3000 10v + v2 = 3000 The v term is v. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 10v + 0.25 + v2 = 3000 + 0.25 Reorder the terms: 0.25 + 10v + v2 = 3000 + 0.25 Combine like terms: 3000 + 0.25 = 3000.25 0.25 + 10v + v2 = 3000.25 Factor a perfect square on the left side: (v + 0.5)(v + 0.5) = 3000.25 Calculate the square root of the right side: 54.77453788 Break this problem into two subproblems by setting (v + 0.5) equal to 54.77453788 and -54.77453788.Subproblem 1
v + 0.5 = 54.77453788 Simplifying v + 0.5 = 54.77453788 Reorder the terms: 0.5 + v = 54.77453788 Solving 0.5 + v = 54.77453788 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = 54.77453788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = 54.77453788 + -0.5 v = 54.77453788 + -0.5 Combine like terms: 54.77453788 + -0.5 = 54.27453788 v = 54.27453788 Simplifying v = 54.27453788Subproblem 2
v + 0.5 = -54.77453788 Simplifying v + 0.5 = -54.77453788 Reorder the terms: 0.5 + v = -54.77453788 Solving 0.5 + v = -54.77453788 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + v = -54.77453788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + v = -54.77453788 + -0.5 v = -54.77453788 + -0.5 Combine like terms: -54.77453788 + -0.5 = -55.27453788 v = -55.27453788 Simplifying v = -55.27453788Solution
The solution to the problem is based on the solutions from the subproblems. v = {54.27453788, -55.27453788}
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